The field of the invention is systems and methods for magnetic resonance imaging (“MRI”). More particularly, the invention relates to systems and methods for fast reconstruction for quantitative susceptibility mapping (“QSM”) using MRI.
Quantifying tissue iron concentration in vivo is important for understanding the role of iron in physiology and in neurological diseases associated with abnormal iron distribution. Excessive iron deposition in subcortical and brain stem nuclei occurs in a variety of degenerative neurological and psychiatric disorders including Alzheimer's disease, Huntington's Chorea, multiple sclerosis, and Parkinson's disease. Postmortem and in vivo studies have also revealed that deep gray matter brain structures accumulate iron at different rates throughout adult aging. Structures that exhibit iron accrual support components of cognitive and motor functioning. To the extent that excessive iron presence may attenuate neuronal function or disrupt connectivity, quantification and location of iron deposition may help explain age-related and disease-related motor slowing and other selective cognitive decline.
Several MRI techniques have been utilized for in vivo iron mapping and quantification. For example, one method capitalizes on the enhanced transverse relaxivity (R2) of iron, by utilizing a field-dependent relaxation rate increase (“FDRI”) approach, whereby R2-weighted imaging is acquired at two different field strengths, attributing a relaxation enhancement at a higher field to iron. While FDRI relies on the modulation of signal intensity in MRI to infer iron concentration, MRI signal phase has also been proposed as a source signal for iron mapping, both by direct evaluation of phase images and reconstruction of magnetic susceptibility images from the phase data. Since local iron concentration is strongly correlated with the magnetic susceptibility, quantification of this paramagnetic property presents a sensitive estimate of iron concentration, although possibly complicated by more uncommon factors, such as pathological manganese deposition. Although phase mapping yields high-resolution, high-SNR data, estimating the underlying magnetic susceptibility suffers from non-local effects and spatial modulation artifacts due to the non-trivial mapping from susceptibility to phase.
Magnetic susceptibility, χ, can be mapped to the observed phase shift in MRI via a well-understood transformation, yet the inverse problem, namely the estimation of χ from phase, is ill-posed due to zeros on a conical surface in the Fourier space of the forward transform. Hence, χ inversion benefits from additional regularization, which is an approach that commonly involves introducing additional information in order to solve an ill-posed problem or to prevent over-fitting.
Recently, regularization methods have been proposed for deriving susceptibility inversion. Specifically, smooth regions in the susceptibility map were promoted to match those of MR image magnitudes by introducing a weighted l2-norm penalty on the spatial gradients of susceptibility, χ. Likewise, another approach regularized the inversion by minimizing the l1-norm of gradients of χ, again weighted with a mask derived from MR image magnitudes. In addition, some proposed methods have used experimented l1-norm and l2-norm regularizations directly on the susceptibility values, rather than posing the minimization on the gradient coefficients.
Still another recent approach has been introduced to stabilize the susceptibility reconstruction problem by acquiring data at multiple orientations and inverting them simultaneously without regularization. Compared to regularized reconstruction techniques that employ a signal prior, such multi-orientation methods yield susceptibility maps with good quality, but at the cost of increased scan time and patient discomfort.
Therefore, given the above, there still remains a need for systems and methods for fast and accurate reconstruction of quantitative susceptibility maps.